well as far as I can tell Wotc has at two different points in time had different opinions on this matter. it used to be CL -1 for regs and -2 for epics, and now it seems too be equal which is sorta lame.Personally, I calculate CR at CL -1 per 5 HD (rounded up). so I make a 7th level Character CR 5, and a 13th level character CR 10.Keeps things pretty solid, especially if you play the NPC tactically or give him some little minions to work with like animal companions with improved grab, goblin mercenaries or just a couple of Howlers for the hell of it and damnit why else did they print CHariot proficiency?

a CR encounter equal to the party's level (Assuming a 'typical' 4 player party of mage, cleric, fighter and rogue), is supposed to consume about 25% of their resources, so a Lvl 3 NPC is indeed a roughly CR3 encounter for 4 Lvl 3 characters (With sufficient handwaving and noise about it being guidelines not strict rules, etc.).

Ensure she has cast Mage Armour before the fight, AC 16. Cast Shield, AC 20. That's 2 1st level spells from an NPC that will be casting 3rd level offensive spells, so no major loss. If she has plenty of spell slots free, you can also cast Blur and Mirror Image from 2nd level. Hell, add in Cat's Grace and Bull's Endurance and that's another 2AC and 10HP. Most of these last 5 minutes, the mage armour 5 hours. There's no excuse not to have Mage Armour on, and as long as she's aware that there are PCs about, 5 minutes for the others is somewhat sensible. You could even have them on scrolls, to reduce the treasure the PCs get if she has the chance to cast them...

She is now actually harder to hit in melee than many melee classes, as well as being immune to magic missiles, and providing confusion of targets for magic users.

Ensure she has Expeditious Retreat packed if she is likely to want to flee.

I have to agree with the whole mage armour and shield specs there, they are sorta the quintessential spells of wizards not dying in combat. but if the person is playing a necromancer, some other stuff works better or at least just as well as the blur and major image. Minions are good gift to the morbidity infatuated. check out heroes of horror, and the summon undead spells. they make for a much more necromancy casting necromancer at lower levels, and personally I like to use shadow spells and dark magic when playing my necromancer's so they have that whole darkness and death thing going as opposed to summoning a ghoul and then hitting the pc's with a bright and shiny color spray.Stuff like death armour, shadow mask, dark-bolt and the like. hard too find and you need like three books, but I can make a necromancer whose spells actually reflect what a necromancer does... which is nice.also, check out the Dread Necromancer class in Heroes of Horror. It... a durable spellcaster.

This is the RAW, but thinking about it this morning, I'm not sure a single equivalent-level NPC will consume 25% of a party's resources. Yes, it's equivalent in strength (disregarding gear...) to 25% of the party, but a party of four should be able to dispose of the NPC fairly easily, due to the benefit of numbers.

RAW certainly say that an NPC PC class is CR(level) and an NPC NPC class (warrior, adept, etc) is CR(level-1).

This works well if you start stacking NPCs up - if you have 4 equivalent level NPCs, then you're getting an EL of level+4, at which point this should be a very tough fight, and would be. Add some minions in to a standard NPC, and again I think it works OK. But a single NPC solo, I'm not sure it works. Then again, I don't think pitting a party against a solo NPC is ever going to be an interesting fight, unless the NPC is higher level than them, or has some other nasty surprises.

The wizard loses initiative. PC Fighter wins, charges the wizard and hits with a greatsword, doing 10 points of damage. PC Rogue also charges, hits with a rapier, doing 11 points of damage (gotta love sneak attack on a flat-footed foe). Wizard drops to the floor. Party has used no resources.

I don't disagree with your scenario; but the problem with a solo NPC is initiative can make such a huge difference. And, of course, wizards do have possibly the best potential to manage maximum damage in the short space of time they might possibly have, and especially with time to prepare, they can be devastating.

Alternatively, your scenario occurs. Fighter charges wizard, but picks the wrong mirror image (all buff spells from my previous post have been cast). Rogue waits, canny to the mirror image thing. PC Wizard casts magic missile, clearing two of the mirror images. Rogue now moves to flank the wizard, but fails to hit the 22AC/20% miss chance required. Cleric cures moderate wounds on himself, leaving himself only 5hp of damage. Wizard takes a 5 foot step back, and casts a fireball on the defensive, easily making the concentration check. PC wizard collapses to the floor, possibly dead. Fighter is staggered, rogue is fine, cleric is again badly damaged. Fighter power attacks the wizard, dealing an impressive 16 damage, but then collapses to the floor. Rogue and cleric both move in to melee, but both fail to connect. Wizard casts burning hands, cleric drops, rogue's luck finally fails and takes 12 damage. Rogue attacks once more, and finally hits, but with no-one to flank with him, only does a measly 4 damage. Thanks to the Bull's Endurance, our wizard still has 3hp left. She casts Cause Fear and the rogue flees. The wizard drinks a potion and then follows the rogue. When the rogue is out of charge range, she fires the first of two magic missiles, certain that the rogue can't attack before she can fire the second one which she is certain will kill him. At an expected 10hp each, she's not wrong...

As others have said, an encounter against a PC class is supposed to be a CR equal to the class levels (NPC classes are CR equal to half their class levels).

Part of the issue is that despite what the game would like to believe, not all PC classes are equal. For example, at low levels spell-casters can be pretty fragile, making them not necessarily CR encounters (since one good hit from the barbarian will likely drop them). Similarly at low levels stuff like a Barbarian or a Fighter can be more dangerous, if only because they deal more damage before they go down.

So while it is probably safe to say that a well-played NPC has CR equal to their class levels, it is also likely that the EL (the encounter level) may be lower based on the conditions of the battle--a low-level wizard caught surprised is going to drop the EL a lot, while a low-level barbarian caught surprised may not as much.

As others have said, an encounter against a PC class is supposed to be a CR equal to the class levels (NPC classes are CR equal to half their class levels).

I once thought that and as a result truecatachresis nearly faced a 6th level Orc Warrior at second level, which I thought was CR3.

For NPC classes it is character level -1. (DMG pages 37 to 38). The Monster Manal (page 294) says that NPC levels are always non-associated which to me always seemed to imply that 2 NPC levels count as +1 CR when advancing an NPC, but I think this only applies to the point when they hit the monster's hit die, at which point the "-1" rule applies like it does out of the box for "0 hit die" PC races.